Radio Telescope Images Sharpened by New Grid-Based Calibration Technique

Scientists are continually refining techniques to mitigate systematic errors in wide-field radio astronomy images. Sebastiaan van der Tol, Sarod Yatawatta, and Bram Veenboer of the Netherlands Institute for Radio Astronomy, alongside David Rafferty from the University of Hamburg, present a novel calibration method utilising image-domain gridding to address direction-dependent effects arising from sources like the ionosphere and beam patterns. Their research overcomes the limitations of traditional facet-based calibration, which requires additional smoothing to reconcile discontinuities in estimated errors. By modelling calibration using sub-grids in Fourier space, this approach delivers a continuous error model, demonstrably improving image quality with LOFAR data and offering a more plausible representation of wide-field systematics.

Image-domain gridding resolves systematic errors in radio interferometer calibration

Scientists have developed a novel calibration technique for radio interferometers that significantly improves image quality across wide fields of view. This breakthrough addresses a longstanding challenge in radio astronomy, where systematic errors originating from the ionosphere and instrument characteristics distort observations.
Traditional calibration methods rely on correcting data in discrete sky directions, requiring additional processing to smooth these corrections and avoid noticeable discontinuities. This work circumvents the need for such post-processing by employing image-domain gridding as the core model for calibration.

Instead of estimating corrections for isolated points in the sky, the research team implemented a calibration process based on a grid system within the Fourier space of the image. This approach inherently creates a continuous, seamless model of systematic errors, eliminating the artificial edges present in conventional facet-based calibration.

By representing calibration parameters as sub-grids in Fourier space, the method automatically reconciles variations in systematic errors without the need for mosaicing or smoothing operations. The resulting images demonstrate enhanced clarity and accuracy, particularly due to the physically plausible nature of the continuous error model.

Results from observations using the Low Frequency Array (LOFAR) demonstrate the efficacy of this new technique. A direct comparison with traditional facet-based calibration reveals a marked improvement in image quality. The team achieved this by estimating direction-dependent errors across the entire field of view, parameterizing them using a basis in spatial space, and directly applying these corrections during image synthesis.

This streamlined process avoids the creation of an intermediate systematic error model, reducing computational complexity and enhancing efficiency. The innovation lies in unifying direction-dependent calibration and imaging into a more cohesive process. Existing methods often treat these as separate steps, leading to potential inconsistencies.

This work utilizes stochastic optimization methods to efficiently minimize calibration problems with a large parameter space, enabling the processing of wide fields of view. While similar approaches exist, this method distinguishes itself through its computational efficiency, achieved by employing a frequentist approach rather than a Bayesian one, and its compatibility with expansive observational areas.

Fourier-space gridding and stochastic optimisation for unified calibration and imaging

A novel calibration technique utilising image-domain gridding forms the basis of this research into wide-field radio interferometry. Rather than employing the conventional approach of estimating and correcting systematic errors along discrete directions in the sky, calibration was performed using a basis representing sub-grids in Fourier space.

This innovative method directly addresses the discontinuities arising from stepwise variations in estimated errors at the edges of traditional ‘facets’, eliminating the need for subsequent smoothing or mosaicing operations. The work aimed to unify direction-dependent calibration and imaging, moving beyond the typical disjointed approach of separate error estimation and correction stages.

Low Frequency Array (LOFAR) data were utilised to validate the proposed technique and facilitate comparison with established facet-based calibration methods. Calibration was achieved through stochastic optimisation, enabling minimisation of complex problems with a large parameter space and demonstrating super-linear convergence.

During calibration, direction-dependent errors across the entire field of view were estimated and parameterised using an arbitrary spatial basis. The resulting A-terms, representing systematic error corrections, were then directly applied during image synthesis, bypassing the creation of an intermediate systematic error model.

This approach differs from existing joint calibration and imaging methods which often parameterise both the sky and instrument systematics simultaneously, or are limited by computational complexity and narrow fields of view. By modelling calibration in the image domain, the research successfully avoids the limitations of piecewise constant models for direction-dependent systematic errors, resulting in demonstrably improved image quality. The study highlights the physical plausibility of the new method and its potential to advance wide-field radio interferometry data processing.

Image fidelity enhancement via image-domain gridding calibration

Researchers developed a novel calibration technique for radio interferometers that eliminates the need for extra processing steps typically required to reconcile systematic errors in wide-field images. This work overcomes the discrete nature of direction-dependent calibration by employing image-domain gridding as the model for calibration, effectively moving from calibration based on discrete sky directions to a basis representing sub-grids in Fourier space.

This approach automatically addresses discontinuities present in traditional facet-based calibration methods. The study utilized data from the Low Frequency Array (LOFAR) to compare the new image-domain gridding calibration (IDG-CAL) with conventional facet-based calibration. Results demonstrate improved image quality stemming from the plausibility of the proposed approach, which avoids the use of piecewise constant models for direction-dependent systematic errors.

The method parameterizes direction-dependent errors across the full field of view using an arbitrary basis in space, directly applying these estimated terms during image synthesis without creating an intermediate systematic-error model. Calibration complexity was reduced through the implementation of stochastic optimization methods, enabling minimization of optimization problems with large parameter spaces and achieving super-linear convergence.

A similarity exists with the work of Roth et al. (2023) in utilizing image-domain gridding for forward model prediction, however, the current method is computationally more efficient due to a frequentist approach, making it compatible with wide fields of view. The research successfully unifies direction-dependent calibration and imaging, differing from existing joint methods by maintaining separate calibration and imaging steps while still estimating full field-of-view errors.

Fourier space gridding delivers continuous calibration for radio interferometry

Researchers have developed a novel calibration technique for radio interferometry that improves image quality by addressing direction-dependent systematic errors. Traditional methods estimate and correct these errors using discrete directions in the sky, requiring additional processing to smooth the resulting data and avoid discontinuities.

This new approach, termed image-domain gridding (IDG), utilises a gridding model in Fourier space to perform calibration, effectively removing the need for smoothing or mosaicing procedures. The IDG-based calibration, IDG-CAL, operates by representing calibration data as sub-grids within the Fourier space, allowing for a continuous correction of systematic errors.

Evaluations using data from the LOFAR telescope demonstrate that IDG-CAL surpasses conventional facet-based calibration, primarily due to its ability to model direction-dependent errors without the limitations of piecewise constant approximations. The method efficiently applies varying corrections and iteratively solves for error terms directly from the observed visibilities.

The authors acknowledge that the computational cost of IDG-CAL may be higher than facet-based methods, although the benefits in image quality currently outweigh this consideration. Future research will likely focus on optimising the computational efficiency of the technique and exploring its application to other radio interferometers and datasets. This advancement offers a clear path towards more accurate and reliable wide-field radio imaging, particularly for complex astronomical sources and surveys.